Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 56, Number 3 (2016), 465-499.
Classification of automorphisms on a deformation family of hyper-Kähler four-folds by -elementary lattices
We give a classification of all nonsymplectic automorphisms of prime order acting on irreducible holomorphic symplectic four-folds deformation equivalent to the Hilbert scheme of two points on a K3 surface, for , and . Our classification relates some invariants of the fixed locus to the isometry classes of two natural lattices associated to the action of the automorphism on the second cohomology group with integer coefficients. In several cases we provide explicit examples. As an application, we find new examples of nonnatural nonsymplectic automorphisms of order .
Kyoto J. Math., Volume 56, Number 3 (2016), 465-499.
Received: 24 March 2014
Revised: 22 April 2015
Accepted: 23 April 2015
First available in Project Euclid: 22 August 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 14C05: Parametrization (Chow and Hilbert schemes) 03G10: Lattices and related structures [See also 06Bxx]
Boissière, Samuel; Camere, Chiara; Sarti, Alessandra. Classification of automorphisms on a deformation family of hyper-Kähler four-folds by $p$ -elementary lattices. Kyoto J. Math. 56 (2016), no. 3, 465--499. doi:10.1215/21562261-3600139. https://projecteuclid.org/euclid.kjm/1471872277